Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and Dynamic Environments

TL;DR

This paper introduces a novel control method using time-varying soft-maximum barrier functions to ensure safety in unknown, dynamic environments by combining local perception data into a unified safety model for robotic navigation.

Contribution

It proposes a closed-form optimal feedback control approach that dynamically combines local safety sets using a smooth soft-maximum function for real-time safe navigation.

Findings

Successfully applied to ground robot and quadrotor systems.

Ensures safety while navigating unknown environments.

Provides a closed-form solution for real-time control.

Abstract

We present a closed-form optimal feedback control method that ensures safety in an a prior unknown and potentially dynamic environment. This article considers the scenario where local perception data (e.g., LiDAR) is obtained periodically, and this data can be used to construct a local control barrier function (CBF) that models a local set that is safe for a period of time into the future. Then, we use a smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single barrier function that models an approximate union of the N most recently obtained local sets. This composite barrier function is used in a constrained quadratic optimization, which is solved in closed form to obtain a safe-and-optimal feedback control. We also apply the time-varying soft-maximum barrier function control to 2 robotic systems (nonholonomic ground robot with nonnegligible inertia, and quadrotor robot), where the objective is to navigate an a priori unknown environment safely and reach a target destination. In these applications, we present a simple approach to generate local CBFs from periodically obtained perception data.